Problem: Simplify the following expression: $r = \dfrac{7}{4z} + \dfrac{5}{2z}$
Solution: In order to add expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $4z$ and $2z$ $\lcm(4z, 2z) = 4z$ $ r = \dfrac{1}{1} \cdot \dfrac{7}{4z} + \dfrac{2}{2} \cdot \dfrac{5}{2z} $ $r = \dfrac{7}{4z} + \dfrac{10}{4z}$ $r = \dfrac{7 +10}{4z}$ $r = \dfrac{17}{4z}$